{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DEJ3GNL5KNCT4B6464E7SHOMQW","short_pith_number":"pith:DEJ3GNL5","canonical_record":{"source":{"id":"1501.01447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-01-07T11:19:00Z","cross_cats_sorted":[],"title_canon_sha256":"f03be0886834f2052d039a205ce44cb15b148cb17b42cd2d33411f36be0dd08c","abstract_canon_sha256":"f62885906718bcbec4b6febbdf5b68bc7b1f81f2d0de3f7b13726a628289f63f"},"schema_version":"1.0"},"canonical_sha256":"1913b3357d53453e07dcf709f91dcc85b89f0783e17b6a55772c677f0fa5e3a2","source":{"kind":"arxiv","id":"1501.01447","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01447","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01447v2","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01447","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"DEJ3GNL5KNCT","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DEJ3GNL5KNCT4B64","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DEJ3GNL5","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DEJ3GNL5KNCT4B6464E7SHOMQW","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-01-07T11:19:00Z","cross_cats_sorted":[],"title_canon_sha256":"f03be0886834f2052d039a205ce44cb15b148cb17b42cd2d33411f36be0dd08c","abstract_canon_sha256":"f62885906718bcbec4b6febbdf5b68bc7b1f81f2d0de3f7b13726a628289f63f"},"schema_version":"1.0"},"canonical_sha256":"1913b3357d53453e07dcf709f91dcc85b89f0783e17b6a55772c677f0fa5e3a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:12.057896Z","signature_b64":"8zO0gO+Tmeop78mgj03uwqZavtsAcDZdfbG1rkoqDqS71y+wDIBA/Z5uKuQs0eg83NU3cuMkBrjqBBdOvYGrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1913b3357d53453e07dcf709f91dcc85b89f0783e17b6a55772c677f0fa5e3a2","last_reissued_at":"2026-05-18T01:20:12.057409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:12.057409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01447","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yl5SGzEaoODcJGHFK7jRiIzFUfb/CNLlT1cewo2k528jOrdGtQTXd3jGn5l3m4cv0mrsPf1NWKnKw29ZiZQFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:05:16.218871Z"},"content_sha256":"33ac8d30cf28f4e809517129791b91f6a98d0c0fcc04ec9187e3353c754f5237","schema_version":"1.0","event_id":"sha256:33ac8d30cf28f4e809517129791b91f6a98d0c0fcc04ec9187e3353c754f5237"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DEJ3GNL5KNCT4B6464E7SHOMQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum mechanics on a curved Snyder space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"R. Strajn, S. Mignemi","submitted_at":"2015-01-07T11:19:00Z","abstract_excerpt":"We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the Born reciprocity for exchange of positions and momenta. Its representations can be obtained starting from those of the Snyder algebra, and exploiting the geometrical properties of the phase space, that can be identified with a Grassmannian manifold. Both the position and momentum operators turn out to have a discrete spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01447","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Imtxd31ipt/JyWkZeQIimxVF8hKT/GHJC6WoxtJF80EP8OgM8jvLGL5a68W9V3z3yyfAAFZSmMNYt0eV/IvDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:05:16.219219Z"},"content_sha256":"49e2b7a51502ecfcd73421b24c0878c8a05fc758158c57fdcb66c351a77362e8","schema_version":"1.0","event_id":"sha256:49e2b7a51502ecfcd73421b24c0878c8a05fc758158c57fdcb66c351a77362e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEJ3GNL5KNCT4B6464E7SHOMQW/bundle.json","state_url":"https://pith.science/pith/DEJ3GNL5KNCT4B6464E7SHOMQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEJ3GNL5KNCT4B6464E7SHOMQW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T11:05:16Z","links":{"resolver":"https://pith.science/pith/DEJ3GNL5KNCT4B6464E7SHOMQW","bundle":"https://pith.science/pith/DEJ3GNL5KNCT4B6464E7SHOMQW/bundle.json","state":"https://pith.science/pith/DEJ3GNL5KNCT4B6464E7SHOMQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEJ3GNL5KNCT4B6464E7SHOMQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DEJ3GNL5KNCT4B6464E7SHOMQW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f62885906718bcbec4b6febbdf5b68bc7b1f81f2d0de3f7b13726a628289f63f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-01-07T11:19:00Z","title_canon_sha256":"f03be0886834f2052d039a205ce44cb15b148cb17b42cd2d33411f36be0dd08c"},"schema_version":"1.0","source":{"id":"1501.01447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01447","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01447v2","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01447","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"DEJ3GNL5KNCT","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DEJ3GNL5KNCT4B64","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DEJ3GNL5","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:49e2b7a51502ecfcd73421b24c0878c8a05fc758158c57fdcb66c351a77362e8","target":"graph","created_at":"2026-05-18T01:20:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the Born reciprocity for exchange of positions and momenta. Its representations can be obtained starting from those of the Snyder algebra, and exploiting the geometrical properties of the phase space, that can be identified with a Grassmannian manifold. Both the position and momentum operators turn out to have a discrete spectrum.","authors_text":"R. Strajn, S. Mignemi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-01-07T11:19:00Z","title":"Quantum mechanics on a curved Snyder space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01447","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:33ac8d30cf28f4e809517129791b91f6a98d0c0fcc04ec9187e3353c754f5237","target":"record","created_at":"2026-05-18T01:20:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f62885906718bcbec4b6febbdf5b68bc7b1f81f2d0de3f7b13726a628289f63f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-01-07T11:19:00Z","title_canon_sha256":"f03be0886834f2052d039a205ce44cb15b148cb17b42cd2d33411f36be0dd08c"},"schema_version":"1.0","source":{"id":"1501.01447","kind":"arxiv","version":2}},"canonical_sha256":"1913b3357d53453e07dcf709f91dcc85b89f0783e17b6a55772c677f0fa5e3a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1913b3357d53453e07dcf709f91dcc85b89f0783e17b6a55772c677f0fa5e3a2","first_computed_at":"2026-05-18T01:20:12.057409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:12.057409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8zO0gO+Tmeop78mgj03uwqZavtsAcDZdfbG1rkoqDqS71y+wDIBA/Z5uKuQs0eg83NU3cuMkBrjqBBdOvYGrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:12.057896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33ac8d30cf28f4e809517129791b91f6a98d0c0fcc04ec9187e3353c754f5237","sha256:49e2b7a51502ecfcd73421b24c0878c8a05fc758158c57fdcb66c351a77362e8"],"state_sha256":"8f83b3fbb262e3798bf4c68181f1b18a9439a6e00d856fbef55a95d98a261e0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sV5Tj6EGsKv9TFSfh90J5js+mpauiYlyJZP1BdebiA872kRuwwH6ldGa3Q7XK/5cttY4F7y17yeYSrHOp/m4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:05:16.221127Z","bundle_sha256":"fd0c77816bd668efa80c7e24621d8285fa37b7bdd7e0fde3e45363acecd49a45"}}